The Random Source Inverse Method and Properties for a Class of Stochastic Differential Equations

CHEN Chen; FENG Xiaoli; CHEN Hanzhang

doi:10.21656/1000-0887.430170

Volume 44 Issue 7

Jul. 2023

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CHEN Chen, FENG Xiaoli, CHEN Hanzhang. The Random Source Inverse Method and Properties for a Class of Stochastic Differential Equations[J]. Applied Mathematics and Mechanics, 2023, 44(7): 847-856. doi: 10.21656/1000-0887.430170

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The Random Source Inverse Method and Properties for a Class of Stochastic Differential Equations

doi: 10.21656/1000-0887.430170

School of Mathematics and Statistics, Xidian University, Xi'an 710126, P.R.China

Received Date: 2022-05-19
Rev Recd Date: 2022-06-28
Publish Date: 2023-07-01

Abstract

Abstract

The random source inverse method and properties for a class of stochastic differential equations driven by the fractional Brownian motion with Hurst index H∈(0, 1). This problem can be obtained from the transform of many stochastic models and is a widely followed problem. For the direct problem, the mild solution to the equation was obtained by means of constant variation, and according to the statistical properties of the mild solution, the well-posedness of the direct problem was discussed. For the inverse problem, some statistics of the random source term were determined from the random data at the final moment, to prove the uniqueness of the inverse problem, and the stability of the inverse problem with a(x) in different ranges was discussed.
- stochastic differential equation,
- fractional Brownian motion,
- inverse source problem,
- uniqueness,
- ill-posedness

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References(17)

References

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